Question

(a) Normally the human body can endure a temperature of \(105^{\circ} \mathrm{F}\) for only short periods of time without permanent damage to the brain and other vital organs. What is this temperature in degrees Celsius? (b) Ethylene glycol is a liquid organic compound that is used as an antifreeze in car radiators. It freezes at \(-11.5^{\circ} \mathrm{C}\). Calculate its freezing temperature in degrees Fahrenheit. (c) The temperature on the surface of the sun is about \(6300^{\circ} \mathrm{C}\). What is this temperature in degrees Fahrenheit?

Short answer

a) 105°F = 40.56°C; b) -11.5°C = 11.3°F; c) 6300°C = 11404°F.

Step-by-step solution

Understanding Temperature Conversion Formulas

To convert temperatures from Fahrenheit to Celsius, use the formula: \(C = \frac{5}{9}(F - 32)\). To convert temperatures from Celsius to Fahrenheit, use the formula: \(F = \frac{9}{5}C + 32\).

Convert 105°F to Celsius

Use the formula \(C = \frac{5}{9}(F - 32)\). Substitute 105 for \(F\): \(C = \frac{5}{9}(105 - 32) = \frac{5}{9}(73)\). Calculate: \(C \approx 40.56\).

Convert -11.5°C to Fahrenheit

Use the formula \(F = \frac{9}{5}C + 32\). Substitute -11.5 for \(C\): \(F = \frac{9}{5}(-11.5) + 32\). Calculate: \(F \approx 11.3\).

Convert 6300°C to Fahrenheit

Use the formula \(F = \frac{9}{5}C + 32\). Substitute 6300 for \(C\): \(F = \frac{9}{5}(6300) + 32\). Calculate: \(F = 11372 + 32 = 11404\).

Key concepts

Fahrenheit to Celsius conversion

Temperature conversion is key in understanding weather reports, medical conditions, and even in cooking recipes. To convert Fahrenheit to Celsius, the formula is \(C = \frac{5}{9}(F - 32)\). This formula tells us how many degrees above or below freezing point (32°F) needs to be adjusted in Celsius scale.

For example, suppose we have a temperature of 105°F. Applying our conversion formula:

• First, subtract 32 from 105, giving us 73.
• Then, multiply 73 by \(\frac{5}{9}\), which equals approximately 40.56°C.

Now you can see how understanding this conversion is crucial for interpreting temperatures that could affect health and safety, like body heat.

Celsius to Fahrenheit conversion

Converting Celsius to Fahrenheit is just as important, especially in settings where Fahrenheit is the primary temperature unit. The conversion formula is \(F = \frac{9}{5}C + 32\). This helps to transform a Celsius temperature to an equivalent Fahrenheit value by accounting for the scale difference and adding the freezing point adjustment.

Consider an example freezing point for ethylene glycol, \(-11.5^{\circ}C\). Here's how we convert it:

• Multiply \(-11.5\) by \(\frac{9}{5}\), resulting in \(-20.7\).
• Add 32 to \(-20.7\), giving approximately 11.3°F.

This process sheds light on how to manage temperature-sensitive substances in engineering and automotive applications.

Temperature conversions in science education

Understanding temperature conversion is vital in science education. It's not just about memorizing formulas, but comprehending the concept of relative temperatures.

Temperature scales serve as common languages in the scientific community, whether discussing the sun's surface or Earth's climates. For instance, the sun's blistering surface temperature of \(6300^{\circ}C\) converts to Fahrenheit using \(F = \frac{9}{5}C + 32\). Calculating, you get:

• Multiply 6300 by \(\frac{9}{5}\) to get 11372.
• Add 32 to find that it equates to 11404°F.

These conversions can help students understand how science concepts apply in real-world contexts, like astronomy and climate science. Being proficient in these calculations strengthens scientific literacy and analytical skills, essential for aspiring scientists.